Yes, but with a supercomputer, you can design a high-yield device and run virtual tests: what we do now that we're signatories to the NTB.
Truth be told, the Japanese Defense Ministry probably has, if not a partially assembled device, certainly blueprints and the ability to machine and assemble all the pieces the moment the Diet gives the okay.
Actually, we could resume nuclear testing if we wanted to do so. The Senate voted down the Comprehensive Test Ban Treaty.